Efficient and Strategy-Proof Multi-Unit Object Allocation with Money: (Non)decreasing Marginal Valuations without Qquasi-Linearity

ISER DP No. 1097, August 2020

39 Pages Posted: 25 Sep 2020 Last revised: 26 Feb 2021

See all articles by Hiroki Shinozaki

Hiroki Shinozaki

Osaka University - Graduate School of Economics

Tomoya Kazumura

University of Tokyo - Graduate School of Economics

Shigehiro Serizawa

Osaka University - Institute of Social and Economic Research (ISER)

Date Written: August 11, 2020

Abstract

We consider the problem of allocating multiple units of an indivisible object among agents and collecting payments. Each agent can receive multiple units of the object, and his (consumption) bundle is a pair of the units he receives and his payment. An agent's preference over bundles may be non-quasi-linear, which accommodates income effects or soft budget constraints. We show that the generalized Vickrey rule is the only rule satisfying efficiency, strategy-proofness, individual rationality, and no subsidy for losers on rich domains with non-decreasing marginal valuations. We further show that if a domain is minimally rich and includes an arbitrary preference exhibiting both decreasing marginal valuations and a positive income effect, then no rule satisfies the same four properties. Our results suggest that in non-quasi-linear environments, the design of an efficient multi-unit auction mechanism is possible only when agents have non-decreasing marginal valuations.

Keywords: Efficiency, Strategy-Proofness, Non-Quasi-Linear Preferences, Non-Decreasing Marginal Valuations, Decreasing Marginal Valuations, Constant Marginal Valuations, Multi-Unit Auctions

JEL Classification: D44, D47, D71, D82

Suggested Citation

Shinozaki, Hiroki and Kazumura, Tomoya and Serizawa, Shigehiro, Efficient and Strategy-Proof Multi-Unit Object Allocation with Money: (Non)decreasing Marginal Valuations without Qquasi-Linearity (August 11, 2020). ISER DP No. 1097, August 2020, Available at SSRN: https://ssrn.com/abstract=3671180 or http://dx.doi.org/10.2139/ssrn.3671180

Hiroki Shinozaki

Osaka University - Graduate School of Economics ( email )

1-7 Machikaneyama
Toyonaka, Osaka, 560-0043
Japan

Tomoya Kazumura

University of Tokyo - Graduate School of Economics ( email )

Tokyo
Japan

Shigehiro Serizawa (Contact Author)

Osaka University - Institute of Social and Economic Research (ISER) ( email )

6-1 Mihogaoka
Ibaraki, Osaka 567-0047
Japan
+81 6 6879 8558 (Phone)
+81 6 6878 2766 (Fax)

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